Chaotic Motion And Control Of Flapping Wing Mechanism With Bearing Clearance

For its extensive applications in military and civilian, bionic flapping wing micro air vehicle (FMAV) has captured special attention of many researchers in recent years. One of key components of FMAV is flapping wing mechanism and its dynamic characteristics affect directly the behaviors of FMAV.Since the bearing clearance in flapping wing mechanism is inevitable, when it run at a higher speed, the elements of kinematic pair will detach temporarily and the impact happens as they contact once again, which will cause a severe vibration and the velocity, acceleration and reaction force of the kinematic pair will change rapidly. The results from other researchers have shown that such chaotic motion will make the aerodynamic force fluctuate and the lift coefficient reduce remarkably, In order to eliminate such bad influence, the chaotic motion and control of flapping wing mechanism are studied in this thesis.The thesis starts with the discussion of Henon system. A method to control chaos, named OGY method is applied to Henon system. It is shown that OGY method is practicable and efficacious. Additionally, it is found that OGY method is sensitive to the target point and response vector, and the system can be controlled to different periodic orbits by varying the target point and response vector. Such of the studying work establishes the base for the controlling of chaotic motion of flapping wing mechanism.The thesis then deal with the chaotic motion and controlling of flapping wing mechanism. Using Dubowsky's impact pair model, the dynamic equation of the mechanism with bearing clearance and spring under the load of aerodynamic force is established. By the phase diagram and Poincare diagram of the motion, the features of chaotic motion have been revealed. It is found that the maximal Lyapunov exponent will increases with the increasing of the flapping frequency of the flapping wing. By constructing stroboscopic time return map, the parameters needed for controlling chaos by OGY method are obtained, and the motion of flapping wing mechanism is successfully controlled from chaotic motion to periodic motion. The constructing of stroboscopic time series improve the efficiency of calculation for the switch point.The dynamic modeling, optimization and simulations in this thesis are conducted utilizing MATLAB.